In this subreddit, we're frequently asked for which course to take next. In the original post it seemed like there is not a cannonical resource for a strict prerequisite listing of common undergraduate math courses.

The problem is, at this point I'm limited by my own experience with these classes, and I've only taken a small fraction of the classes we would like to cover.

Therefore, I'm asking for help. I'm going to post the current .dot file in the comments section and we can edit it and add courses and change arrows and color code collectively.

The things that need to be done as I see them are:

Add all course topics that are part of the undergrad math requirement at some college (I've missed some)

Choose which lines should be solid and which should be dotted. I think that we should use a solid line only when a course is always a prerequisite and a dotted line for when it is sometimes a prerequisite.

Create a blurb for each topic area (idea: /u/kcufllenroc) including favorite textbooks for the course, the wikipedia page and some standard topics included in a first course.

Find a place to post the final result so it can be linked from the sidebar, or a better way to continuously edit the curriculum. I think if we get to a point where we generally agree we can make a post Part III and just link that.

I agree. In fact ODEs should have a linear algebra dependence as well (although perhaps a dotted line?) because you need to know about eigenvalues/eigenvectors in order to solve first order linear systems.

Also, although I like the idea of an "Intro to proofs" course, such a course is almost never a mandatory prerequisite to all the subsequent courses. Making it mandatory creates a bottleneck in someone's undergrad education.

I don't disagree with regards to an intro to proofs course. My undergrad university had one and it created the exact bottleneck you talk about. I'd be open to taking it off, but part of the reason I want this chart is because some of the time the people asking the question have to take just such a course in order to progress further (e.g. What do I do after calculus?)

Georgia state offered it because math majors would drop out due to not having the basic idea of what math is really about. They claimed it helped get everyone on the same page, even though some students thought it was to easy. It also got people an intro to algebraic structures, set theory, and set theory notation.

I love this, but I think you should probably add labels to some courses to clarify contents. For instance, is calc 3 multivariable, or is that in calc 2? (matters for dependencies.) I'm also unsure what the probability classes cover- do schools have two probability classes after intro? (that are not stats, so don't require linear algebra?)

You could also include:
Game theory, requiring linear algebra and probability. Also, graph theory, requiring linear algebra and proofs.

there are also some more applied math areas you might include, such as numerical methods.

My experience differs slightly. It's especially likely to be named differently in community colleges and/or those on a non semester system, again, in my experience. One place had calc 1-2, then advanced calculus, which was calc 3, then advanced calc 2, which was analysis.

That chart doesn't have anything that strikes me as being incorrect, so good job. At my university, we have a required "History of Mathematics" course, which is offered every two years and can be taken after Discrete I (I believe)
As for as number three goes, I'm doing some digging around my texts books (I've kept them all) and here's a few.

Calc 1,2 and three have what I call "the standard issue" James Stewart (X current edition. I think there's 8 or 9) It's an extremely popular textbook, although don't feel as if you need to stick to it because it definitely isn't perfect.
My advisor is teaching a summer math class, and he simply used this online textbook for calculus one

I took them concurrently and it wasn't too bad. After the first week it felt like I was using two different tool boxes for the two courses. Most analysis courses have a rudimentary discussion of metric space topology that'll get you familiar with the terminology (open/closed/compact etc.)

Not sure exactly what your analysis 1 and 2 are considered to cover, But as far as anything in analysis with more than one variable linear algebra is immensely necessary. Particularly I'm thinking of the change of variables formula for multivariate integration, which relies heavily on determinants.

I applaud the idea of making a dependency chart of sorts, but I think some changes should be made.

First of all, the nodes should be topics (like "group theory" or "multivariable calculus") rather than names of courses (like "algebra I" or "calculus II"). I realize that many of these course names are pretty standard, but there is certainly some variety in the content of courses with similar names, depending on the school. Some schools don't even have courses with these names.

Second, so-called "mathematical maturity" should not be accounted for in the dependency chart - it should be assumed that the student picks it up along the way. In other words: drop "intro to proofs". Is "intro to proofs" really necessary for linear algebra and euclidean geometry? (By the way, is even "calculus I" necessary for these courses?)